Place Pawns So No Three Ever Line Up
Henry Dudeney set this chessboard challenge in 1900: place as many pawns as possible on an 8x8 board so that no three of them ever fall on a single straight line — at any angle, not just rows, columns or diagonals. Keep adding pawns and eventually a line of three becomes unavoidable. What's the most you can place first?
Reveal the answer
Sixteen pawns — exactly two per row and two per column, arranged so no three ever align. Dudeney posed the problem in 1900, and it's since become a long-studied question in combinatorial geometry: for larger n x n grids, whether 2n points can always be placed this way remains an open problem beyond the cases mathematicians have checked.
— Henry Dudeney, No-three-in-line problem — Posed 1900; included in Amusements in Mathematics (1917)
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